In 1966, Jacques Heyman provided a rigorous base for applying Limit Analysis to masonry structures. Most of the computational approaches based on his theory rely on Safe Theorem and can address kinematical problems only for simple geometries. So far, no computational tools have been developed for addressing the Kinematical Problem directly, for generic structures and for different mechanical problems (stability, effects of overloading and of settlements even in large displacements). With this aim, a new computational tool, compas_prd, has been developed. It is an open-source, Python-based tool, framed within the COMPAS Masonry. It is based on the Piecewise Rigid Displacement (PRD) method and represents a natural extension of Heyman's theory to continuum mechanics. The PRD method couples the Kinematical Problem with the Equilibrium Problem, allowing the search for a mechanism and its corresponding internal stress states even in large displacements. Both the kinematical and the equilibrium problems are framed as linear programming problems, thus, allowing fast computational solving. Looking at a semicircular arch, two studies are proposed to outline the abilities of compas_prd. In the first, we perform a PRD displacement capacity analysis following two different approaches. With the second study, we explore the spectrum of all mechanisms/thrusts exhibited by a semicircular arch subjected to a generic foundation displacement.